Problem: The grades on a history midterm at Oak are normally distributed with $\mu = 73$ and $\sigma = 5.5$. Vanessa earned a $58$ on the exam. Find the z-score for Vanessa's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Vanessa's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{58 - {73}}{{5.5}}} $ ${ z \approx -2.73}$ The z-score is $-2.73$. In other words, Vanessa's score was $2.73$ standard deviations below the mean.